Mathematical Physics

2402 Submissions

[2] viXra:2402.0139 [pdf] replaced on 2024-05-16 19:41:00

Clean CUT: A Clean Cosmological Unified Theory Resolving the Hierarchy Problem

Authors: Oussama Basta
Comments: 21 Pages.

In this paper, we propose a new theoretical framework called "Clean CUT" (Clean Cosmological Unified Theory) that offers a paradigm-shifting perspective on the fundamental nature of the universe. By seamlessly unifying gravitation, electromagnetism, spin, and quantum mechanics, Clean CUT provides a comprehensive description of the fundamental forces and resolves long-standing issues in physics.
Category: Mathematical Physics

[1] viXra:2402.0030 [pdf] submitted on 2024-02-06 08:36:58

On Discrete Hopf Fibrations, Grand Unification Groups, the Barnes-Wall, Leech Lattices, and Quasicrystals

Authors: Carlos Castro
Comments: 13 Pages.

A discrete Hopf fibration of $S^{15}$ over $S^8$ with $S^7$ (unit octonions) as fibers leads to a $16D$ Polytope $P_{16}$ with $4320$ vertices obtained from the convex hull of the $16D$ Barnes-Wall lattice $ Lambda_{16}$. It is argued how a subsequent $2-1$ mapping (projection) of $ P_{16}$ onto a $8D$-hyperplane might furnish the $2160$ vertices of the uniform $2_{41}$ polytope in $8$-dimensions, and such that one can capture the chain sequence of polytopes $ 2_{41}, 2_{31}, 2_{21}, 2_{11}$ in $ D = 8,7,6,5$ dimensions, leading, respectively, to the sequence of Coxeter groups $ E_8, E_7, E_6, SO(10) $ which are putative GUT group candidates. An embedding of the $E_8 oplus E_8 $ and $ E_8 oplus E_8 oplus E_8$ lattice into the Barnes-Wall $ Lambda_{16}$ and Leech $Lambda_{24}$ lattices, respectively, is explicitly shown. From the $16D$ lattice $ E_8 oplus E_8$ one can generate two separate families of Elser-Sloane $4D$ quasicrystals (QC's) with $ H_4$ (icosahedral) symmetry via the ``cut-and-project" method from $ 8D$ to $ 4D$ in each separate $E_8$ lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC's $ {cal Q} times {cal Q} $ spanning an $8D$ space. Similarly, from the $24D$ lattice $ E_8 oplus E_8 oplus E_8$ one can generate the Cartesian product of three Elser-Sloane $4D$ quasicrystals (QC's) $ {cal Q} times {cal Q} times {cal Q} $ with $ H_4$ symmetry and spanning a $12D$ space.
Category: Mathematical Physics